Abstract: This one day meeting fosters research interactions among mathematicians, engineers and physicists who develop and apply techniques from harmonic analysis. Theoretical topics of interest include: Fourier analysis, wavelets, Gabor systems (time-frequency analysis), frames, Riesz bases, compressed sensing, approximation theory, X-ray type transforms.
Applications of interest include: all kinds of signal and image analysis, processing and reconstruction, both analogue and digital.
This conference is supported in part by the Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program. PI members may use IMA/PI funds to support travel of their personnel to this conference.
All interested researchers are welcome. There is no registration fee. Travel funding is available for participants based in the U.S.
For more information:
http://mathcs.slu.edu/~johnson/imaha/

Abstract: We will review the notion of turbulence, present a mathematical theory for it (in 2D), and then see how it can be twisted to have fun with a 3D system (Rayleigh-Benard heat convection problem).

The existence of smooth solutions to fractal Burgers equation with critical exponent

Abstract: In this talk, we present a piece of joint work of Chi Hin Chan and Magdalena Czubak, in which we establish the existence of smooth solutions to fractal Burgers equation with critical exponent by applying the parabolic De Giorgi's method as developed by Luis Caffarelli and Alexis Vasseur. In the talk, we will make a parallel comparison between our work on fractal Burgers' equation with critical exponent and the work by Caffarelli and Vasseur in their paper "Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation.

Turbulence transition in shear flows: what can we learn from pipe flow?

Abstract: According to textbook wisdom, flow down a pipe becomes turbulent near a Reynolds number of about 2000. This simple statement misses many subtleties of the transition: the absence of a linear stability of the laminar flow, the sensitive dependence on perturbations that sometimes succeed and sometimes fail to induce turbulence and the unexpected observation that the turbulent state, once achieved, is not persistent but can decay. All these observations are compatible with the formation of a strange saddle in the state space of the system. I will focus on three aspects: on the appearance of 3-d coherent states, on the information contained in lifetime statistics and on results on the boundary between laminar and turbulent regions. They suggest a generic structuring of state space in flows where turbulent and laminar flow coexist, such as plane Couette flow, Poiseuille flow and perhaps even boundary layers.

On spider-man and film casting: the mathematics of free liquid fibers and films in elongation

Abstract: In this lecture we give an overview of the
mathematical theory of free liquid fibers and films of
highly viscous liquids in fiber spinning and film casting. The governing equations to be discussed arise as the slender body approximation of the Navier-Stokes equations with moving boundary as 1D or 2D nonlinear
coupled hyperbolic-elliptic systems of pdes. Topics
of interest in this presentation include existence and uniqueness results, failure of fiber breakup in the
purely viscous regime, and spectral determinacy/regularity of the linearized film equations. Some open questions will be
motivated.

Abstract: Mixing by stirring can be measured in a variety of ways including tracer particle dispersion, the scalar flux-gradient relationship, or via suppression of scalar density variation in the presence of inhomogeneous sources and sinks. The mixing efficacy of a flow is often expressed in terms of enhanced diffusivity and quantified as an effective diffusion coefficient. In this work we compare and contrast these various notions of effective diffusivity. Via thorough examination of a simple shear flow mixing a scalar sustained by a steady source-sink distribution, we explore apparent inconsistencies and propose a conceptual approach that captures some compatible features of these different models and measures of mixing.

Experimental determination of the likelihood of catastrophic instability in Gaussian elimination

Abstract: The growth factor of a matrix quantifies the amount of potential error growth when a linear system is solved by Gaussian elimination with partial pivoting. While the growth factor has a maximum of 2n-1 for an n × n matrix, experience suggests the occurrence of matrices with exponentially large growth factors is extremely rare. To add computational evidence, we implemented a multicanonical Monte Carlo method to explore the tails of growth factor probability distributions for random matrices.

Abstract: Controllability refers to the ability to steer a system from a
prescribed initial state to a desirable final state. The lecture
will give an overview of recent results on the controllability
of flows of viscoelastic fluids by means of a prescribed body
force or prescribed motion of the boundary.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.

Abstract: When we look out on a clear night, the universe seems infinite. Yet this infinity might be an illusion. During the first half of the presentation, computer games will introduce the concept of a "multiconnected universe." Interactive 3D graphics will then take the viewer on a tour of several possible shapes for space. Finally, we'll see how recent satellite data provide tantalizing clues to the true shape of our universe. The only prerequisites for this talk are curiosity and imagination. For middle school and high school students, people interested in astronomy, and all members of the university and surrounding communities.

Visitors in Residence

Nusret Balci

University of Minnesota

9/1/2009 - 8/31/2010

Jennifer Beichman

University of Michigan

9/1/2009 - 5/31/2010

Richard J. Braun

University of Delaware

9/1/2009 - 12/20/2009

Maria-Carme T. Calderer

University of Minnesota

9/1/2009 - 6/30/2010

Tamra Carpenter

Rutgers University

11/1/2009 - 11/3/2009

Chi Hin Chan

University of Minnesota

9/1/2009 - 8/31/2010

Xianjin Chen

University of Minnesota

9/1/2008 - 8/31/2010

Eric Choate

University of North Carolina

10/10/2009 - 11/10/2009

L. Pamela Cook

University of Delaware

9/6/2009 - 12/20/2009

Michael Earl Cromer Jr

University of Delaware

9/1/2009 - 12/31/2009

Charles Doering

University of Michigan

8/15/2009 - 6/15/2010

Bruno Eckhardt

Philipps-Universität Marburg

11/16/2009 - 11/20/2009

Randy H. Ewoldt

University of Minnesota

9/1/2009 - 8/31/2010

David Finn

Rose-Hulman Institute of Technology

9/1/2009 - 11/23/2009

Sandip Ghosal

Northwestern University

9/21/2009 - 12/12/2009

Michael D. Graham

University of Wisconsin

9/1/2009 - 12/22/2009

Thomas C. Hagen

University of Memphis

9/1/2009 - 12/31/2009

Yunkyong Hyon

University of Minnesota

9/1/2008 - 8/31/2010

Mark Iwen

University of Minnesota

9/1/2008 - 8/31/2010

Srividhya Jeyaraman

University of Minnesota

9/1/2008 - 8/31/2010

Lijian Jiang

University of Minnesota

9/10/2008 - 8/31/2010

Mihailo Jovanovic

University of Minnesota

9/11/2009 - 6/10/2010

Markus Keel

University of Minnesota

7/21/2008 - 6/30/2010

Hyejin Kim

University of Minnesota

9/1/2009 - 8/31/2010

Pawel Konieczny

University of Minnesota

9/1/2009 - 8/31/2010

Ronald G. Larson

University of Michigan

9/12/2009 - 12/22/2009

Chiun-Chang Lee

National Taiwan University

10/22/2009 - 6/30/2010

Young-Ju Lee

Rutgers University

9/11/2009 - 12/31/2009

Marta Lewicka

University of Minnesota

9/1/2009 - 6/30/2010

Yi Li

Stevens Institute of Technology

9/16/2009 - 12/17/2009

Yongfeng Li

University of Minnesota

9/1/2008 - 8/31/2010

Tai-Chia Lin

National Taiwan University

11/29/2009 - 12/10/2009

Zhi (George) Lin

University of Minnesota

9/1/2009 - 8/31/2010

Chun Liu

University of Minnesota

9/1/2008 - 8/31/2010

Ellen K. Longmire

University of Minnesota

9/1/2009 - 6/30/2010

Yasunori Maekawa

Kobe University

9/7/2009 - 3/1/2010

Krishnan Mahesh

University of Minnesota

9/1/2009 - 6/30/2010

Kara Lee Maki

University of Minnesota

9/1/2009 - 8/31/2010

Vasileios Maroulas

University of Minnesota

9/1/2008 - 8/31/2010

Yoichiro Mori

University of Minnesota

9/1/2009 - 6/30/2010

Walter Morris

Rutgers University

11/1/2009 - 11/3/2009

Monika Nitsche

University of New Mexico

9/1/2009 - 12/22/2009

Cecilia Ortiz-Duenas

University of Minnesota

9/1/2009 - 8/31/2010

Hans G. Othmer

University of Minnesota

9/1/2009 - 6/30/2010

Michael Renardy

Virginia Polytechnic Institute and State University

9/1/2009 - 12/20/2009

Yuriko Renardy

Virginia Polytechnic Institute and State University

9/1/2009 - 12/20/2009

Juan Mario Restrepo

University of Arizona

8/11/2009 - 6/15/2010

Rolf Ryham

Rice University

11/19/2009 - 11/27/2009

Fadil Santosa

University of Minnesota

7/1/2008 - 6/30/2010

Arnd Scheel

University of Minnesota

9/1/2009 - 6/30/2010

George R Sell

University of Minnesota

9/1/2009 - 6/30/2010

Tsvetanka Sendova

University of Minnesota

9/1/2008 - 8/31/2010

Shuanglin Shao

University of Minnesota

9/1/2009 - 8/31/2010

Daniel Spirn

University of Minnesota

9/8/2009 - 6/1/2010

Paul H. Steen

Cornell University

10/15/2009 - 12/15/2009

Panagiotis Stinis

University of Minnesota

9/1/2009 - 6/30/2010

Huan Sun

Pennsylvania State University

8/16/2009 - 12/15/2009

Vladimir Sverak

University of Minnesota

9/1/2009 - 6/30/2010

Mark Taylor

Sandia National Laboratories

9/1/2009 - 12/22/2009

Jean-Luc Thiffeault

University of Wisconsin

9/1/2009 - 6/30/2010

Chad Michael Topaz

Macalester College

9/1/2009 - 6/30/2010

Changyou Wang

University of Kentucky

9/1/2009 - 6/15/2010

Jeffrey Weeks

NONE

11/11/2009 - 11/13/2009

Sijue Wu

University of Michigan

9/1/2009 - 6/5/2010

Wei Xiong

University of Minnesota

9/1/2008 - 8/31/2010

Tsuyoshi Yoneda

University of Minnesota

9/4/2009 - 8/31/2010

Weigang Zhong

University of Minnesota

9/8/2008 - 8/31/2010

Legend:Postdoc or Industrial PostdocLong-term Visitor

IMA Affiliates:

Arizona State University, Boeing, Corning Incorporated, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Kent State University, Korea Advanced Institute of Science and Technology (KAIST), Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger Cambridge Research, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pennsylvania, University of Pittsburgh, University of Tennessee, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute